1. Warm Up 4

2. Simulations
Unit 8 Day 4

3. Intro to Simulations
What is a simulation? Using a computer to determine outcomes of random events When would we need to use them? When conducting an experiment in real life is impractical or want to save time, money, or reduce effort.

4. List of Commands needed
randInt( lower bound, upper bound, amount of times) MATH → PRB menu → option 5
sum( nd → STAT → MATH menu → option 5
L1, L2, etc nd → STAT → choose from NAMES menu
=, and other inequality symbols 2nd → MATH → choose from TEST menu
and, or nd → MATH → LOGIC menu →
choose from menu

5. Simulating a Die Roll
Since we don’t have dice, we will use a random number generator on our calculators as a replacement. Why? Because the generator will randomly produce different integers that we need. How? By plugging in the specific information into the “formula” to fit our problem. In the calculator, the random number generator is located under MATH → PRB → 5: randInt( Once you have selected 5: randInt( , there are three values that needs to be plugged in: randInt(lower bound, upper bound, number of values)

6. Suppose we want to simulate rolling a die.
First, what are all the possible outcomes when rolling a die?
1, 2, 3, 4, 5, 6
Second, plug in the given information that we know about our die.
randInt(1, 6, 1)
Third, press ENTER to determine what number you “rolled”
If you continue to press ENTER you will see your 2nd, 3rd, 4th, etc. “roll”

7. NOW! Let’s generate 10 rolls at once.
We will enter our 10 rolls into L1. Thus, go to:
STAT→ Edit → highlight L1 → ENTER → MATH → PRB → 5: randInt(1, 6, 10) → ENTER
Now find how many 1’s, 2’s, 3’s, etc. was “rolled” in this simulation.
Go to: 2nd → STAT → MATH → 5:sum( → 2nd → 1 → 2nd → MATH → 1: = → #
1 = 2 = 3 = 4 = 5 = 6 =
What is the simulated probability for each amount?

8. Now simulate 100 rolls by.. randInt(1, 6, 100) → ENTER
What is the simulated probability for each amount?
1 = 2 = 3 = 4 = 5 = 6 =
Now simulate 999 rolls by.. randInt(1, 6, 999) → ENTER
What happens to the probability (percentage of occurrence) as the number of rolls increase? Why?
The probabilities are getting closer to 16.6%, because the more simulations taken the closer the probabilities reach their true probability (16.6%).

9. Simulating the roll of TWO dice (at the same time)
If you roll two dice and add them together, which outcomes are possible?
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
What do we need to do to simulate rolling two dice and adding them together?
Set up a 2nd list of numbers in L2
Set It Up! Then find the simulated probability of each outcome.
Sum(L1+L2 = #)

10. Baseball Scenario 500 at-bats in a typical season
A player has 1/10 chance of hitting a homerun and has a 3/10 chance of hitting the ball without being a homerun
How could we set up the generator to represent this scenario?
randInt(1, 10, 500)
Let 1 represent hitting a homerun
Let 2, 3 and 4 represent make a hit, but not a homerun

11. Baseball Scenario
How many homeruns did the player get? What’s this probability?
sum(L1 = 1)
How many hits without a homerun did the player get? What’s this probability?
sum(L1=2 or L1=3 or L1=4)
How many hits AND homeruns did the player get? What’s this probability?
sum(L1=1 and (L1=2 or L1=3 or L1=4)
How many times did the player not get a hit or a homerun? What’s this probability?
sum(L1= 5 or L1= 6 or L1= 7 or L1= 8 or L1= 9 or L1 = 10)
500 – previous answer

12. Kohl’s Store Scenario 50 days working part time at Kohl’s
Cashiers are required to solicit credit card applications and have people sign up for the program.
A cashier has 1/8 chance of meeting their credit card apps. goal each day they work. L1
A cashier has a separate chance of 2/3 of meeting their goal each day they work L2
How would we set up the generators for each situation?
L1 = randInt(1, 8, 50) - Let 1 represent when a cashier meets their credit card goal
L2 = randInt(1, 3, 50) - Let 1 and 2 represent when a cashier meets their goal

13. Kohl’s Store Scenario
How many days of work was the credit card app. goal met?
Sum(L1 = 1)
How many days of work was the goal met?
Sum(L2 = 1 or L2 = 2)
How many days of work was both the credit card app. goal and the goal met together?
Sum(L1 = 1 and (L2 = 1 or L2 = 2))